• ETRI Journal
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• v.22 no.4
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• pp.25-31
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• 2000

Design of secure and efficient public-key encryption schemes under weaker computational assumptions has been regarded as an important and challenging task. As far as ElGamal-type encryption schemes are concerned, some variants of the original ElGamal encryption scheme based on weaker computational assumption have been proposed: Although security of the ElGamal variant of Fujisaki-Okamoto public -key encryption scheme and Cramer and Shoup's encryption scheme is based on the Decisional Diffie-Hellman Assumption (DDH-A), security of the recent Pointcheval's ElGamal encryption variant is based on the Computational Diffie-Hellman Assumption (CDH-A), which is known to be weaker than DDH-A. In this paper, we propose new ElGamal encryption variants whose security is based on CDH-A and the Elliptic Curve Computational Diffie-Hellman Assumption (EC-CDH-A). Also, we show that the proposed variants are secure against the adaptive chosen-ciphertext attack in the random oracle model. An important feature of the proposed variants is length-efficiency which provides shorter ciphertexts than those of other schemes.

• Bulletin of the Korean Mathematical Society
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• v.46 no.2
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• pp.303-309
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• 2009

Cryptographic protocols depend on the hardness of some computational problems for their security. Joux briefly summarized known relations between assumptions related bilinear map in a sense that if one problem can be solved easily, then another problem can be solved within a polynomial time [6]. In this paper, we investigate additional relations between them. Firstly, we show that the computational Diffie-Hellman assumption implies the bilinear Diffie-Hellman assumption or the general inversion assumption. Secondly, we show that a cryptographic useful self-bilinear map does not exist. If a self-bilinear map exists, it might be used as a building block for several cryptographic applications such as a multilinear map. As a corollary, we show that a fixed inversion of a bilinear map with homomorphic property is impossible. Finally, we remark that a self-bilinear map proposed in [7] is not essentially self-bilinear.

• Journal of the Korea Society of Computer and Information
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• v.23 no.2
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• pp.53-61
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• 2018

In this paper, the author proposes an efficient group key agreement scheme in a mobile environment where group members frequently join and leave. This protocol consists of basic protocols and general ones and is expected to be suitable for communications between a mobile device with limited computing capability and a key distributing center (or base station) with sufficient computing capability. Compared with other schemes, the performance of the proposed protocol is a bit more efficient in the aspects of the overall cost for both communication and computation where the computational efficiency of the scheme is achieved by using exclusive or operations and a one-way hash function. Also, in the aspect of security, it guarantees both forward and backward secrecy based on the computational Diffie-Hellman (CDH) assumption so that secure group communication can be made possible. Furthermore, the author proves its security against a passive adversary in the random oracle model.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.13 no.5
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• pp.147-157
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• 2003

We often use cryptographic systems on small devices such as mobile phones, smart cards and so on. But such devices are delicate against the tlreat of key exposure of secret keys. To reduce the damage caused by exposure of secret keys stored on such devices, the concept of forward security is introduced. In this Paper, we present a new forward secure signature scheme based on Gap Diffie-Hellman groups. Our scheme achieves security against chosen-message attacks under the computational Diffie-Hellman assumption in the random oracle model.

• Journal of Communications and Networks
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• v.12 no.6
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• pp.592-599
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• 2010

In recent years, significant improvements have been made to the techniques used for analyzing satellite communication and attacking satellite systems. In 2003, a research team at Los Alamos National Laboratory, USA, demonstrated the ease with which civilian global positioning system (GPS) spoofing attacks can be implemented. They fed fake signals to the GPS receiver so that it operates as though it were located at a position different from its actual location. Moreover, Galileo in-orbit validation element A and Compass-M1 civilian codes in all available frequency bands were decoded in 2007 and 2009. These events indicate that cryptography should be used in addition to the coding technique for secure and authenticated satellite communication. In this study, we address this issue by using an authenticated key-exchange protocol to build a secure and authenticated communication channel for satellite communication. Our protocol uses identity-based cryptography. We also prove the security of our protocol in the extended Canetti-Krawczyk model, which is the strongest security model for authenticated key-exchange protocols, under the random oracle assumption and computational Diffie-Hellman assumption. In addition, our protocol helps achieve high efficiency in both communication and computation and thus improve security in satellite communication.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.15 no.1
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• pp.41-55
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• 2005

A group key agreement protocol allows a group of user to share a key which may later be used to achieve certain cryptographic goals. In this paper, we propose a new scalable two-round ID-based group key agreement protocol which would be well fit to a Pay-TV system, additionally. to the fields of internet stock quotes, audio and music deliveries, software updates and the like. Our protocol improves the three round poop key agreement protocol of Nam et al., resulting in upgrading the computational efficiency by using the batch verification technique in pairing-based cryptography. Also our protocol simplifies the key agreement procedures by utilizing ID-based system. We prove the security of our protocol under the Computational Diffie-Hellman assumption and the Bilinear Decisional Diffie-Hellman assumption. Also we analyze its efficiency.

• The KIPS Transactions:PartC
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• v.12C no.7 s.103
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• pp.949-958
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• 2005

In the paper we study key agreement schemes when a party needs to establish a session key with each of several parties, thus having multiple session keys. This situation can be represented by a graph, tailed a key graph, where a vertex represents a party and an edge represents a relation between two parties sharing a session key. graphs to establish all session keys corresponding to all edges in a key graph simultaneously in a single session. A key agreement protocol of a key graph is a natural extension of a two-party key agreement protocol. We propose a new key exchange model for key graphs which is an extension of a two-party key exchange model. using the so-called randomness re-use technique which re-uses random values to make session keys for different sessions, we suggest two efficient key agreement protocols for key graphs based on the decisional Diffie-Hellman assumption, and prove their securities in the key exchange model of key graphs. Our first scheme requires only a single round and provides key independence. Our second scheme requires two rounds and provides forward secrecy. Both are proven secure In the standard model. The suggested protocols are the first pairwise key agreement protocols and more efficient than a simple scheme which uses a two-party key exchange for each necessary key. Suppose that a user makes a session key with n other users, respectively. The simple scheme's computational cost and the length of the transmitted messages are increased by a factor of n. The suggested protocols's computational cost also depends on n, but the length of the transmitted messages are constant.

• Journal of Communications and Networks
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• v.8 no.4
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• pp.461-474
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• 2006

A group key exchange protocol is a cryptographic primitive that describes how a group of parties communicating over a public network can come up with a common secret key. Due to its significance both in network security and cryptography, the design of secure and efficient group key exchange protocols has attracted many researchers' attention over the years. However, despite all the efforts undertaken, there seems to have been no previous systematic look at the growing problem of key exchange over combined wired and wireless networks which consist of both stationary computers with sufficient computational capabilities and mobile devices with relatively restricted computing resources. In this paper, we present the first group key exchange protocol that is specifically designed to be well suited for this rapidly expanding network environment. Our construction meets simplicity, efficiency, and strong notions of security.

• Journal of Communications and Networks
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• v.10 no.1
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• pp.10-17
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• 2008

In traditional digital signature schemes, certificates signed by a trusted party are required to ensure the authenticity of the public key. In Asiacrypt 2003, the concept of certificateless signature scheme was introduced. The advantage of certificateless public key cryptography successfully eliminates the necessity of certificates in the traditional public key cryptography and simultaneously solves the inherent key escrow problem suffered in identity-based cryptography. Recently, Yap et al. proposed an efficient certificateless signature scheme and claimed that their scheme is existentially unforgeable in the random oracle model. In this paper, we show that the certificateless signature scheme proposed by Yap et al. is insecure against public key replacement attacks. Furthermore, we propose an improved certificateless signature scheme, which is existentially unforgeable against adaptive chosen message attacks under the computational Diffie-Hellman assumption in the random oracle model and provide the security proof of the proposed scheme.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.10 no.2
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• pp.881-896
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• 2016

Certificate-based cryptography is a useful public key cryptographic primitive that combines the merits of traditional public key cryptography and identity-based cryptography. It not only solves the key escrow problem inherent in identity-based cryptography, but also simplifies the cumbersome certificate management problem in traditional public key cryptography. In this paper, by giving a concrete attack, we first show that the certificate-based encryption scheme without bilinear pairings proposed by Yao et al. does not achieve either the chosen-ciphertext security or the weaker chosen-plaintext security. To overcome the security weakness in Yao et al.'s scheme, we propose an enhanced certificate-based encryption scheme that does not use the bilinear pairings. In the random oracle model, we formally prove it to be chosen-ciphertext secure under the computational Diffie-Hellman assumption. The experimental results show that the proposed scheme enjoys obvious advantage in the computation efficiency compared with the previous certificate-based encryption schemes. Without costly pairing operations, it is suitable to be employed on the computation-limited or power-constrained devices.